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27 . 93 / 65 . 82
= 27 . (32)3 / (2.3)5 . (23)2
= 27 . 36 / 25 . 35 . 26
= 27 . 36 / 211 . 35
= 3/24
= 3/16
1. Tính
\(\frac{2^7\cdot9^3}{6^5\cdot8^2}=\frac{2^7\cdot\left(3^2\right)^3}{\left(3\cdot2\right)^5\cdot\left(2^3\right)^2}=\frac{2^7\cdot3^6}{3^5\cdot2^5\cdot2^6}=\frac{2^7\cdot3^5\cdot3}{3^5\cdot2^{11}}=\frac{2^7\cdot3}{2^7\cdot2^4}=\frac{3}{2^4}=\frac{3}{16}\)
2. Tìm x
\(8^x:4^x=4\Rightarrow\left(8:4\right)^x=4\Rightarrow2^x=4\Rightarrow x=2\)
3. Ta có : \(222^{555}=\left(2\cdot111\right)^{555}=2^{555}\cdot111^{555}=\left(2^5\right)^{111}\cdot111^{555}=32^{111}\cdot111^{555}\)(1)
\(555^{222}=\left(5\cdot111\right)^{222}=5^{222}\cdot111^{222}=\left(5^2\right)^{111}\cdot111^{222}=25^{111}\cdot111^{222}\)(2)
Từ (1) và (2) ta thấy : 32 > 25 => 32111 > 25111 và 111555 > 111222 ( vì 555 > 222)
Vậy 222555 > 555222
\(\frac{2^7.9^3}{6^5.8^2}=\frac{2^7.3^6}{2^5.3^5.2^6}=\frac{3}{2^4}=\frac{3}{16}\)
đặt biểu thức là A=\(\frac{2^7.9^3}{6^5.8^2}\)=\(\frac{2^7.3^6}{3^5.2^5.2^6}\)=\(\frac{3}{2^4}\)
\(\frac{2^7.9^3}{6^5.8^2}=\frac{2^7.\left(3^2\right)^3}{2^5.3^5.\left(2^3\right)^2}\)
\(=\frac{2^7.3^6}{2^{11}.3^5}=\frac{3}{2^4}=\frac{3}{16}\)
\(\frac{2^7.9^3}{6^5.8^2}\)
\(=\frac{2^7.\left(3^2\right)^3}{\left(2.3\right)^5.\left(2^3\right)^2}=\frac{2^7.3^6}{2^5.3^5.2^6}=\frac{3}{2^4}=\frac{3}{16}\)
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\(\frac{2^7.9^3}{6^5.8^2}\)
\(=\)\(\frac{2^7.\left(3^2\right)^3}{\left(2.3\right)^5.\left(2^3\right)^2}\)
\(=\)\(\frac{2^7.3^6}{2^5.3^5.2^6}\)
\(=\)\(\frac{2^7.3^6}{2^{11}.3^5}\)
\(=\)\(\frac{3}{2^4}=\frac{3}{16}\)